If a right cylinder with a radius of 2 cm has a volume of `100picm^(3)`, what is the height, in centimeters, of the cylinder?

Options

A. `20`
B. `25`
C. `40`
D. `50`

Answer

To find the height of the cylinder, we will use the formula for the volume of a cylinder, which is given by:

\[ V = \pi r^2 h \]

where:
- \( V \) is the volume of the cylinder,
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

### Step 1: Identify the given values
From the problem, we have:
- Radius \( r = 2 \) cm
- Volume \( V = 100 \pi \) cm³

### Step 2: Substitute the known values into the volume formula
We can substitute the values of \( V \) and \( r \) into the volume formula:

\[ 100 \pi = \pi (2)^2 h \]

### Step 3: Simplify the equation
First, calculate \( (2)^2 \):

\[ (2)^2 = 4 \]

Now substitute this back into the equation:

\[ 100 \pi = \pi \cdot 4 \cdot h \]

### Step 4: Cancel out \( \pi \) from both sides
Since \( \pi \) is present on both sides of the equation, we can cancel it out:

\[ 100 = 4h \]

### Step 5: Solve for \( h \)
Now, we can solve for \( h \) by dividing both sides by 4:

\[ h = \frac{100}{4} \]

Calculating this gives:

\[ h = 25 \]

### Conclusion
The height of the cylinder is \( 25 \) cm.

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